Problem: The mean of one set of five numbers is 13, and the mean of a separate set of six numbers is 24. What is the mean of the set of all eleven numbers?
Solution: The sum of the numbers from the first set is $5\cdot 13=65$.  The sum of the numbers from the second set is $24\cdot 6 = 144$.  The sum of all the numbers in the set is $144+65=209$, so the average of the 11 numbers in the set is $209/11=\boxed{19}$.